Abstract
The nature of magnetohydrodynamic waves in structured magnetic fields is discussed, with particular reference to sunspots. The modes of oscillation of an isolated flux tube are reviewed. We consider the nature of surface waves on an interface between two isothermal gases, one of which is embedded within a horizontal magnetic field.
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References
Abdelatif, T. E. (1988) ’Surface and body waves in magnetic flux tubes’, Astrophys. J. 333, 395–406.
Abels-van Maanen, A. E. P. M. and Weenik, M. P. H. (1979) Radio Sci. 14, 301.
Adam, J. A. (1977) ’On the occurrence of critical levels in solar magnetohydrody- namics’, Solar Phys. 52, 293–307.
Adam, J. A. (1982) ’Asymptotic solutions and spectral theory of linear wave equations’, Physics Reports 86, 217–316.
Adam, J. A. (1986) ’Critical layer singularities and complex eigenvalues in some differential equations of mathematical physics’, Physics Reports 142, 263–356.
Antia, H. M. and Chitre, S. M. (1979) ’Waves in the sunspot umbra’, Solar Phys. 63, 67–78.
Appert, K., Gruber, R. and Vaclavik, J. (1974) ’Continuous spectra of a cylindrical magnetohydrodynamic equilibrium’, Physics Fluids 17,1471–1472.
Beckers, J. M. and Tallant, P. E. (1969) ’Chromospheric inhomogeneities in sunspot umbrae’, Solar Phys. 7, 351–365.
Bernstein, I. B. and Book, D. L. (1983) ’Effect of compressibility on the Rayleigh- Taylor instability’, Phys. Fluids 26, 453–458.
Bodo, G., Rosner, R, Ferrari, A. and Knobloch, E. (1989) ’On the stability of magnetized rotating jets: The axisymmetric case’, Astrophys. J. 341, 631–649.
Bogdan, T. B. (1992) ’Sunspot seismology: the interaction of a sunspot with solar p-modes’, these proceedings.
Braun, D. C., Duvall, T. L. and Labonte, B. J. (1987) ’Acoustic absorption by sunspots’, Astrophys. J. 319, L27–31.
Braun, D. C., Duvall, T. L. and Labonte, B. J. (1988) ’The absorption of high-degree p-mode oscillations in and around sunspots’, Astrophys. J. 335, 1015–1025.
Braun, D. C., Labonte, B. J. and Duvall, T. L. (1990) ’The spatial distribution of p-mode absorption in active regions’, Astrophys. J. 354, 372–381.
Braun, D. C., Labonte, B. J., Duvall, T. L. and Ryutova, M. P. (1991) ’A possible mechanism for enhanced absorption of p-modes in sunspot and plage regions’, Astrophys. J., preprint.
Browning, P. K. (1991) ’Mechanisms of solar coronal heating’, Plasma Phys. and Controlled Fusion 33, 539–571.
Cadez, V. M. and Okretic, V. K. (1989) ’Leakage of MHD surface waves in structured media’, J. Plasma Phys. 41, 23–30.
Cally, P. S. (1985) ’Magnetohydrodynamic tube waves: Waves in fibrils’, Australian J. Phys. 38, 825–837.
Cally, P. S. (1986) ’Leaky and non-leaky oscillations in magnetic flux tubes’, Solar Phys. 103, 277–298.
Cally, P. S. (1991) ’Phase-mixing and surface waves: a new interpretation’, J. Plasma Phys. 45, 453–479.
Cally, P. S. and Adam, J.A. (1983) ’On photospheric and chromospheric penumbral waves’, Solar Phys. 85, 97–111.
Campbell, W. R. and Roberts, B. (1989) ’The influence of a chromospheric magnetic field on the solar p- and f-modes’, Astrophys. J. 338, 538–556.
Chandrasekhar, S. (1961) Hydrodynamic and Hydromagnetic Stability, Oxford University Press, Oxford.
Chen, L. and Hasegawa, A. (1974) ’Plasma heating by spatial resonance of Alfvén wave’, Phys. Fluids 17, 1399–1403.
Chitre, S. M. (1992) ’Theory of umbral oscillations and penumbral waves’, these proceedings.
Chitre, S. M. and Davila, J. M. (1991) ’The resonant absorption of p-modes by sunspots with twisted magnetic fields’, Astrophys. J. 371, 785–792.
Coulson, C. A. (1955) Waves, Oliver and Boyd, Edinburgh.
Cowling, T. G. (1976) Magnetohydrodynamics, Adam Hilger, Bristol.
Davila, J. M. (1987) ’Heating of the solar corona by the resonant absorption of Alfvén waves’, Astrophys. J. 317, 514–521.
Davila, J. M. (1990) ’Sunspot seismology theory’, in E. R. Priest and V. Krishan (eds.), Basic Plasma Processes on the Sun, Kluwer Academic Publishers, Dordrecht, pp. 149–157.
Davila, J. M. (1991) ’Resonance absorption heating’, in P. Ulmschneider, E. R. Priest and R. Rosner (eds.), Mechanisms of Chromospheric and Coronal Heating, Springer-Verlag, Heidelberg, pp. 464–479.
Edwin, P. M. and Roberts, B. (1983) ’Waves in a magnetic cylinder’, Solar Phys. 88, 179–191.
Einaudi, G. and Mok, Y. (1987) ’Alfvén wave dissipation in the solar atmosphere’, Astrophys. J. 319, 520–530.
Evans, D. J. (1990) The Effects of Magnetic Fields on Oscillations in the Solar Atmosphere, Ph. D. thesis, St Andrews University, pp. 194.
Evans, D. J. and Roberts, B. (1990a) ’The oscillations of a magnetic flux tube and its application to sunspots’, Astrophys. J. 348, 346–356.
Evans, D. J. and Roberts, B. (1990b) ’The influence of a chromospheric magnetic field on the frequencies of solar p- and f-modes: II. Uniform chromospheric field’, Astrophys. J. 356, 704–719.
Evans, D. J. and Roberts, B. (1991) ’The sensitivity of a chromospherically induced p- and f-mode frequency shift to the height of the magnetic canopy’, Astrophys. J. 371, 387–395.
Ferraro, V. C. A. and Plumpton, C. (1958) ’Hydromagnetic waves in a horizontally stratified atmosphere’, Astrophys. J. 127, 459–476.
Giovanelli, R. G. (1972) ’Oscillations and waves in sunspots’, Solar Phys. 27, 71–79.
Goedbloed, J. P. (1971) ’Stabilization of magnetohydrodynamic instabilities by forcefree magnetic fields I. Plane plasma layer’, Physica 53, 412–444.
Goedbloed, J. P. (1983) Lecture Notes in Magnetohydrodynamics, Rijnhuizen Report 83–145, Assoc. Euratom — FOM, pp. 1–289.
Goedbloed, J. P. (1984) ’Plasma-vacuum problems in magnetohydrodynamics’, Physica 12D, 107–132.
Goedbloed, J. P. and Hagenbeuk, H. J. L. (1972) ’Growth rates of instabilities of a diffuse linear pinch’, Phys. Fluids 15, 1090–1101.
Gonzalez, A. G. and Gratton, J. (1991) ’Magnetoacoustic surface gravity waves’, Solar Phys. 134, 211–232.
Goossens, M (1991) ’Magnetohydrodynamic waves and wave heating in non-uniform plasmas’, in E.R. Priest and A.W. Hood (eds.), Advances in Solar System Magnetohydrodynamics, Cambridge University Press, Cambridge, pp. 137–172.
Grossmann, W. and Tataronis, J. (1973) Z. Physik. 261, 217.
Grossmann, W. and Smith, R. A. (1988) ’Heating of solar coronal loops by resonant absorption of Alfvén waves’, Astrophys. J. 332, 476–498.
Hain, K. and Lüst, R. (1958) Z. Naturforsch. 13a, 936.
Heyvaerts, J. and Priest, E. R. (1983) ’Coronal heating by phased-mixed Alfvén waves’, Astron. Astrophys. 117, 220–234.
Hollweg, J. V. (1982) ’On the origin of solar spicules’, Astrophys. J. 257, 345–353.
Hollweg, J. V. (1986) ’Energy and momentum transport by waves’, in B. Buti (ed.) Advances in Space Plasma Physics, World Scientific, Singapore, p.77.
Hollweg, J. V. (1987a) ’Resonant absorption of magnetohydrodynamic surface waves: Physical discussion’, Astrophys. J. 312, 880–885.
Hollweg, J. V. (1987b) ’Resonant absorption of magnetohydrodynamic surface waves: Viscous effects’, Astrophys. J. 320, 875–873.
Hollweg, J. V. (1988) ’Resonance absorption of solar p-modes by sunspots’, Astrophys. J. 335, 1005–1014.
Hollweg, J. V. (1990a) ’Heating of the solar corona’, Computer Phys. Reports 12, 205–232.
Hollweg, J. V. (1990b) ’MHD waves on solar magnetic flux tubes’, in C. T. Russell, E. R. Priest and L. C. Lee (eds.), Physics of Magnetic Flux Ropes, AGU: Washington, Geophys. Mono. 58, pp. 23–31.
Hollweg, J. V. (1991) ’Alfvén waves’, in P. Ulmschneider, E. R. Priest and R. Rosner (eds.), Mechanisms of Chromospheric and Coronal Heating, Springer-Verlag, Heidelberg, pp. 423–434.
Ionson, J. A. (1978) ’Resonant absorption of Alfvénic surface waves and the heating of solar coronal loops’, Astrophys. J. 226, 650–673.
Jain, R. and Roberts, B. (1991a) ’Magnetoacoustic surface waves at a single interface’, Solar Phys. 133, 263–280.
Jain, R. and Roberts, B. (1991b) ’Magnetoacoustic surface waves’, in P. Ulmschneider, E. R. Priest and R. Rosner (eds.), Mechanisms of Chromospheric and Coronal Heating, Springer-Verlag, Heidelberg, pp. 511–513.
Kalkofen, W. (1990) ’The heating of the quiet solar chromosphere’, in E. R. Priest and V. Krishan (eds.), Basic Plasma Processes on the Sun, Kluwer Academic Publishers, Dordrecht, pp. 197–206.
Kruskal, M. and Schwarzschild, M. (1954) ’Some instabilities of a completely ionized plasma’, Proc. Roy. Soc. (London) A223, 348–360.
Lee, M. A. and Roberts, B. (1986) ’On the behaviour of hydromagnetic surface waves’, Astrophys. J. 301, 430–439.
Libbrecht, K. G., Woodward, M.F. and Kaufman, J. M. (1990) ’Frequencies of solar oscillations’, Astrophys. J. Suppl. 74, 1127–1149.
Lighthill, M. J. (1960) ’Studies on magneto-hydrodynamic waves and other anisotropic motions’, Phil. Trans. Roy. Soc. A252, 397–430.
Lites, B. W. (1986a) ’Photoelectric observations of chromospheric sunspot oscillations. III. Spatial distribution of power and frequency in umbrae’, Astrophys. J. 301, 992–1004.
Lites, B. W. (1986b) ’Photoelectric observations of chromospheric sunspot oscillations. IV. The Ca II H line and He I A10830’, Astrophys. J. 301, 1005–1017.
Lites, B. W. (1988) ’Photoelectric observations of chromospheric sunspot oscillations. V. Penumbral oscillations’, Astrophys. J. 334, 1054–1065.
Lites, B. W. (1992) ’Observations of oscillations in sunspots’, these proceedings.
Lites, B. W., White, O. R. and Packman, D. (1982) ’Photoelectric observations of propagating sunspot oscillations’, Astrophys. J. 253, 386–392.
Lou, Y.-Q. (1988) ’Viscous magnetohydrodynamic modes and p-mode absorption by sunspots’, in Proc. Symp. Seismology of the Sun and Sun-like Stars, ESA SP-286, Noordwijk, pp. 305–310.
Lou, Y.-Q. (1990) ’Viscous magnetohydrodynamic modes and p-mode absorption’, Astrophys. J. 350, 452–462.
McKenzie, J. F. (1970) ’Hydromagnetic oscillations of the geomagnetic tail and plasma sheet’, J. Geophys. Res., Space Phys. 75, 5331–5339.
Miles, A. J. (1991) Magnetohydrodynamic Surface Waves in the Solar Atmosphere, Ph. D. thesis, St Andrews University, pp. 197.
Miles, A. J., Allen, H. R. and Roberts, B. (1991) ’Magnetoacoustic-gravity surface waves. II. Uniform magnetic field’, Solar Phys., in press.
Miles, A. J. and Roberts, B. (1989) ’On the properties of magnetoacoustic surface waves’, Solar Phys. 119, 257–278.
Miles, A. J. and Roberts, B. (1991a) ’The f-mode and MHD surface waves’, in P. Ulmschneider, E. R. Priest and R. Rosner (eds.) Mechanisms of Chromospheric and Coronal Heating, Springer-Verlag, Heidelberg, pp. 508–510.
Miles, A. J. and Roberts, B. (1991b) ’Magnetoacoustic-gravity surface waves. I. Constant Alfvén speed’, Solar Phys., in press.
Moore, R. and Rabin, D. (1985) ’Sunspots’, Ann. Rev. Astron. Astrophys. 23, 239–266.
Moreno-Insertis, F. and Spruit, H. C. (1989) ’Stability of sunspots to convective motions. I. Adiabatic instability’, Astrophys. J. 342, 1158–1171.
Nocera, L., Leroy, B. and Priest, E. R. (1984) ’Phase mixing of propagating Alfvén waves’, Astron. Astrophys. 133, 387–394.
Nye, A. H. and Thomas, J. H. (1974) ’The nature of running penumbral waves’, Solar Phys. 38, 399–413.
Nye, A. H. and Thomas, J. H. (1976a) ’Solar magneto-atmospheric waves. I. An exact solution for a horizontal magnetic field’, Astrophys. J. 204, 573–581.
Nye, A. H. and Thomas, J. H. (1976b) ’Solar magneto-atmospheric waves. II. A model for running penumbral waves’, Astrophys. J. 204, 582–588.
Parker, E. N. (1974) ’The nature of the sunspot phenomenon I: Solutions of the heat transport equation’, Solar Phys. 36, 249–274.
Parker, E. N. (1979a) ’Sunspots and the physics of magnetic flux tubes. I. The general nature of the sunspot’, Astrophys. J. 230, 905–913.
Parker, E. N. (1979b) Cosmical Magnetic Fields, Oxford University Press, Oxford.
Parker, E. N. (1983) ’The propagation of torsion along flux tubes subject to dynamical nonequilibrium’, Geophys. Astrophys. Fluid Dynamics 24, 245–272.
Parker, E. N. (1987) ’Why do stars emit X-rays?’, Physics Today 40, 36–42.
Parker, E. N. (1991a) ’Heating solar coronal holes’, Astrophys. J. 372, 719–727.
Parker, E. N. (1991b) ’The phase mixing of Alfvén waves, coordinated modes, and coronal heating’, Astrophys. J. 376, 355–363.
Poedts, S., Goossens, M. and Kerner, W. (1990) ’On the efficiency of coronal loop heating by resonant absorption’, Astrophys. J. 360, 279–287.
Rae, I. C. and Roberts, B. (1981) ’Surface waves and the heating of the corona’, Geophys. Astrophys. Fluid Dynamics 18, 197–226.
Rae, I. C. and Roberts, B. (1982) ’Pulse propagation in a magnetic flux tube’, Astrophys. J. 256, 761–767.
Rayleigh, Lord (1877) The Theory of Sound, Dover, New York (reprinted by Dover, 1945), vol. 1, chap. X.
Roberts, B. (1980) ’Developpement recent dans la theorie des ondes MHD parfaites dans les milieux presentant une structure magnetique’, Ann. De Physique 5, 453– 481.
Roberts, B. (1981a) ’Wave propagation in a magnetically structured atmosphere; I. Surface waves at a magnetic interface’, Solar Phys. 69, 27–38.
Roberts, B. (1981b) ’Wave propagation in a magnetically structured atmosphere; II. Waves in a magnetic slab’, Solar Phys. 69, 39–56.
Roberts, B. (1981c) ’Waves in magnetic structures’, in L. E. Cram and J. H. Thomas (eds.) Physics of Sunspots, Sacramento Peak Observatory, Sunspot (New Mexico), pp. 360–383.
Roberts, B. (1985)’Magnetohydrodynamic waves’, in E. R. Priest (ed.), Solar System Magnetic Fields, Reidel, Dordrecht, pp. 37–79.
Roberts, B. (1986) ’Dynamical processes in magnetic flux tubes’, in W. Deinzer, M. Knölker and H. Voight (eds.), Small-Scale Magnetic Flux Concentrations in the Solar Photosphere, Vandenhoeck & Ruprecht, Gottingen, pp. 169–190.
Roberts, B. (1987) ’On MHD solitons in jets’, Astrophys. J. 318, 590–594.
Roberts, B. (1988) ’Solar magnetohydrodynamics’, in B. Buti (ed.), Cometary and Solar Plasmas Physics, World Scientific, Singapore, pp. 1–80.
Roberts, B. (1990a) ’Properties and models of photospheric flux tubes’, in C. T. Russell, E. R. Priest and L. C. Lee (eds.), Physics of Magnetic Flux Ropes, AGU: Washington, Geophys. Mono. 58, pp. 113–132.
Roberts, B.(1990b) ’Waves in magnetic flux tubes’, in E. R. Priest and V. Krishan (eds.), Basic Plasma Processes on the Sun, Kluwer Academic Publishers, Dordrecht, pp. 159–174.
Roberts, B. (1990c) ’Oscillations in the sun’, in B. Buti (ed.), Solar and Planetary Plasma Physics, World Scientific, Singapore, pp. 1–31.
Roberts, B. (1991a) ’Magnetohydrodynamic surface waves’, in P. Ulmschneider, E. R. Priest and R. Rosner (eds.), Mechanisms of Chromospheric and Coronal Heating, Springer-Verlag, Heidelberg, pp. 494–507.
Roberts, B. (1991b) ’Magnetohydrodynamic waves in the sun’, in E.R. Priest and A.W. Hood (eds.), Advances in Solar System Magnetohydrodynamics, Cambridge University Press, Cambridge, pp. 105–136.
Roberts, B., Edwin, P. M. and Benz, A. O. (1984) ’On coronal oscillations’, Astrophys. J. 279, 857–865.
Roberts, B. and Webb, A. R. (1978) ’Vertical motions in an intense magnetic flux tube’, Solar Phys. 56, 5–35.
Roberts, B. and Webb, A. R. (1979) ’Vertical motions in an intense magnetic flux tube: On the slender flux tube approximation’, Solar Phys. 64, 77–92.
Rosenthal, C. (1990) ’Absorption of acoustic waves in monolithic and fibril sunspot models’, Solar Phys. 130, 313–335.
Ryutov, D. D. and Ryutova, M. P. (1976) ’Sound oscillations in a plasma with magnetic filaments’, Sov. Phys. J.E.T.P. 43, 491–497.
Ryutova, M. P. (1990a) ’Waves and oscillations in magnetic fluxtubes’, in J. O. Stenflo (ed.), Solar Photosphere: Structure, Convection and Magnetic Fields , IAU Symp. 138, Reidel, pp. 229–249.
Ryutova, M. P. (1990b) ’Nonlinear waves in flux tubes’, in E. R. Priest and V. Krishan (eds.), Basic Plasma Processes on the Sun, Kluwer Academic Publishers, Dordrecht, pp. 175–186.
Ryutova, M. P. and Persson, M. (1984) ’Dispersion properties and enhanced dissipation of MHD-oscillations in a plasma with random inhomogeneities’, Physica Scripta 29, 353–359.
Sakurai, T., Goossens, M. and Hollweg, J. V. (1991a) ’Resonant behaviour of MHD waves on magnetic flux tubes; I. Connection formulae at the resonant surfaces’Solar Phys. 133, 227–245.
Sakurai, T., Goossens, M. and Hollweg, J. V. (1991b) ’Resonant behaviour of MHD waves on magnetic flux tubes; II. Absorption of sound waves by sunspots’, Solar Phys. 133, 247–262.
Scheuer, M.A. and Thomas, J.H. (1981) ’Umbral oscillations as resonant modes of magneto-atmospheric waves’, Solar Phys. 71, 21–38.
Sedlacek, Z. (1971) ’Electrostatic oscillations in a cold inhomogeneous plasma. I. Differential equation approach’, J. Plasma Phys. 5, 239–263.
Small, L. M. and Roberts, B. (1984) ’On running penumbral waves’, in Hydromag- netics of the Sun, ESA SP-220, pp. 257–259.
Southwood, D. J. (1974) ’Some features of field line resonances in the magnetosphere’, Planet. Space Sci. 22, 483.
Spruit, H. C. (1981) ’Magnetic flux tubes’, in S. Jordan (ed.), The Sun as a Star, NASA SP-450, Washington, pp. 385–412.
Spruit, H. C. (1982) ’Propagation speeds and acoustic damping of waves in magnetic flux tubes’, Solar Phys. 75, 3–17.
Spruit, H. C. and Roberts, B. (1983) ’Magnetic flux tubes on the sun’, Nature 304, 401–406.
Summers, D. (1976) ’Gravity modified sound waves in a conducting stratified atmosphere’, Quart. J. Mech. Appl. Math. 29, 117–126.
Tataronis, J. A. and Grossmann, W. (1973) ’Decay of MHD waves by phase mixing. I. The sheet pinch in plane geometry’, Z. Physik 261, 203–216.
Tayler, R. J. (1957) ’The influence of an axial magnetic field on the stability of a constricted gas discharge’, Proc. Phys. Soc. (London) B70, 1049–1063.
Thomas, J. H. (1983) ’Magneto-atmospheric waves’, Ann. Rev. Fluid Mech. 15, 321–343.
Thomas, J. H. (1985) ’Hydrodynamic waves in the photosphere and chromosphere’, in H .U. Schmidt (ed.), Theoretical Problems in High Resolution Solar Physics, Max Planck Institute: Munich, MPA 212, pp. 126–149.
Thomas, J. H., Cram, L. E. and Nye, A. H. (1982) ’Five-minute oscillations as a subsurface probe of sunspot structure’, Nature 297, 485–487.
Thomas, J. H., Cram, L. E. and Nye, A. H. (1984) ’Dynamical phenomena in sunspots. I. Observing procedures and oscillatory phenomena’, Astrophys. J.285 368–380.
Uberoi, C. (1982) ’A note on the existence of Alfvén surface waves’, Solar Phys. 78, 351–354.
Wentzel, D. G. (1979) ’Hydromagnetic surface waves on cylindrical fluxtubes’, Astron. Astrophys. 76, 20–23.
Wilson, P. R. (1980) ’The general dispersion relation for the vibration modes of magnetic flux tubes’, Astron. Astrophys. 87, 121–125.
Wittmann, A. (1969) ’Some properties of umbral flashes’, Solar Phys. 7, 366–369.
Yu, C. P. (1965) ’Magneto-atmospheric waves in a horizontally stratified conducting medium’, Phys. Fluids 8, 650–656.
Zirin, H. and Stein, A. (1972) ’Observations of running penumbral waves’, Astrophys. J. Lett. 178, L85–87.
Zhugzhda, Y. D. and Dzhalilov, N. S. (1984) ’Magneto-acoustic-gravity waves on the sun; III. The theory of running penumbral waves’, Aston. Astrophys. 133, 333–340.
Zhugzhda, Y. D., Locans, V. and Staude, J. (1983) ’Seismology of sunspot atmospheres’, Solar Phys. 82, 369–378.
Zhugzhda, Y. D., Locans, V. and Staude, J. (1987) ’The interpretation of oscillations in sunspot umbrae’, Astron. Nachr. 308, 257–269.
Zhugzhda, Y. D., Staude, J. and Locans, V. (1984) ’A model of the oscillations in the chromosphere and transition region above sunspot umbrae’, Solar Phys. 91, 219–234.
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Roberts, B. (1992). Magnetohydrodynamic Waves in Structured Magnetic Fields. In: Thomas, J.H., Weiss, N.O. (eds) Sunspots: Theory and Observations. NATO ASI Series, vol 375. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-2769-1_13
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